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Simulation of Powered Resonance Tubes: Effects of Pressure Ratio and Freestream Flow

A.B. Cain*

Innovative Technology Applications Company Chesterfield, MO,

E.J. Kerschen†

University of Arizona Tucson, AZ,

and

G. Raman‡ and S. Khanafseh∗ ∗ Illinois Institute of Technology

Chicago, IL

Copyright 2002 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. * Associate Fellow AIAA, President † Senior Member AIAA, Professor ‡ Associate Fellow AIAA, Associate Professor ∗ ∗ Student member AIAA, Graduate student

ABSTRACT Flow simulations have been performed as part of our effort to better understand powered resonance tube behavior. Scaled simulations of the powered resonance tube have produced reasonable correspondence to laboratory experiments, in terms of the frequency and amplitude of the resonant response. The simulations suggest new insights into the complexity and details of the flowfield. The simulations show that the flow in the integration slot is primarily on the resonance tube side, with almost no flow on the supply tube side of the integration slot. The numerical results suggest that the acoustic waves from the resonance in the resonance tube drive an unsteady separation at the supply tube. The unsteady separation at the supply tube in turn drives the observed large oscillations in the shock structure. The unsteady

separation seems to be a key aspect of the resonance phenomena. Very recently it has been discovered that for shallow resonance tubes, the pressure ratio affects the response frequency. Also, the resonance tube is found to impose strong pressure disturbances in a Mach 0.5 boundary layer flow. The presence of the Mach 0.5 external stream and boundary layer reduces the resonance frequency by about 12%, relative to the case without an external stream.

INTRODUCTION The Department of Defense, DARPA and the Air Force in particular, are moving future warfighter capabilities forward by application of new technologies. One of these new technologies that offers important new capabilities is Active Flow Control (AFC). One of the most critical requirements for the application of AFC is the

1st Flow Control Conference24-26 June 2002, St. Louis, Missouri

AIAA 2002-2821

Copyright © 2002 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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development of actuators with high bandwidth and authority. This paper reports simulation results that were developed in a STTR Program that is focused on producing a new Powered Resonance Tube (PRT) actuator with high bandwidth capabilities and strong authority. The PRT actuator consists of an open-closed tube resonator, excited by a high-speed jet that impinges normally on the open end of the tube. An integration slot lies between the exit plane of the driving jet and the open end of the resonance tube. The unsteady flow produced by the PRT actuator exits from the open edge of the integration slot. The STTR program involves hardware advances, computational simulations and analytical modeling. Together these efforts provide new understanding of the flow physics and guidance for future prototype and production designs of the PRT actuator. Active Flow Control techniques can basically be separated into two classes. The first class (AFC(I)) involves the use of unsteady forcing to excite instability waves of laminar flows, or the large-scale structures of turbulent flows. AFC(I) techniques have been explored extensively in the past decade. A recent review article that discusses many of these advances is presented by Nishri & Wygnanski (1998). The second class of active flow control techniques (AFC(II)), which have been developed more recently, involves the use of actuators to force turbulent boundary and free-shear layers at high frequencies in the Kolmogorov inertial subrange (see Wiltse & Glezer 1998 and Cain et al. 2001). While these two classes of active flow control techniques have different actuator bandwidth requirements, we believe that PRT actuators hold promise for both. Recent applications of the PRT actuator (e.g. Stanek et al. 2000, 2001) have focused on high frequency excitation (AFC(II)). However, acoustic excitation has been used by many researchers to directly control instabilities (AFC(I)) and separation (see Greenblatt & Wygnanski 2000). Since powered resonance tubes produce very high acoustic levels, we believe that the high bandwidth PRT actuator has enormous promise as both a high frequency actuator (AFC(II)) and an instability control actuator (AFC(I)), with tremendous control authority in both applications.

Recent progress in experimental exploration of the PRT includes the visualization studies of Kastner and Samimy (2002). Progress in developing advanced high-bandwidth PRT actuator hardware is presented in Raman, Khanafseh & Cain (2002). Progress in simulating PRT actuator flowfields in the absence of an external stream is presented in Cain, Kerschen & Raman (2002). In the present paper, we consider the effects of the nozzle pressure ratio, and the influence of an external freestream flow and boundary layer. In the following section, we discuss our progress in the simulation of PRT actuator flowfields. The formulation of the computational problem and numerical method are summarized. The results to date, which include the case of an actuator flowfield in the absence of an external stream, the role of nozzle pressure ratio, and the influence of an external stream, are then summarized. SIMULATIONS OF THE POWERED RESONANCE TUBE ACTUATOR

AXISYMMETRIC GEOMETRY IDEALIZATION

The geometry fabricated in the laboratory has a number of complexities that would require an unreasonably large grid and enormous computational resources to simulate. In order to do meaningful simulations with reasonable computational resource requirements, simplifying approximations are required. The first such approximation is to assume an axisymmetric geometry and flowfield.

The basic geometry for the computation consists of a supply tube feeding an axisymmetric integration slot and resonance tube. The external geometry and acoustic radiation are also axisymmetric. The supply tube begins with a ½” diameter at the reservoir end and tapers conically to a ¼” diameter constant section. The supply tube has a brief flare at the exit into the integration slot. The conical section and the constant diameter section are both ½” long.

The grid for the supply tube, integration slot, and resonance tube is illustrated in Fig. 2. The axis of symmetry is along the bottom of the grid. The grid in the supply tube, integration slot, and

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resonance tube has nominally square cells roughly 0.00625” on a side. The lower left horizontal region is the supply tube (zone 1). The vertical segment is the integration slot (zone 2). At the upper boundary between zones 1 and 2 the chamfer in the supply tube is evident. It plays an important role in the resonance phenomena. The right horizontal segment is the resonance tube (zone 3). The full grid for these calculations is illustrated in Fig. 3; the upper region (zone 4) is for farfield propagation. The inner cylindrical surface of zone 4, which the integration slot intersects, is all solid wall except for the integration slot hole. The external boundary layer (when present) is on this surface. Three sides of zone 4 are attached to “buffer zones” where damping is applied to minimize any acoustic wave reflection. These “buffer zones” all extend approximately 3 acoustic wavelengths and the acoustic waves appear fully attenuated by the time they reach the outermost boundaries. In zone 4, the cells gradually expand from the small cells of regions 1, 2 and 3 (0.00625” on a side) to larger cells that are roughly 0.1” on a side. The acoustic waves have roughly 280 cells per wavelength in the supply tube, integration slot, and resonance tube, and at least 16 cells per wavelength at the far edges of the “inner farfield” grid. When a Mach 0.5 stream and external boundary layer are included in the model, a 3/8" wall perpendicular to the surface is inserted near the upstream boundary of the computational domain. The purpose of the wall is to thicken the boundary layer and increase the Reynolds number. The flow reattaches before reaching the integration slot. With the present grid the boundary layer flow is still stable according to linear theory (Reδ*~320 at the resonance tube). Higher Reynolds numbers cannot be run with the present grid without degrading the resolution of the unsteady shock motion. Grid refinement and algorithm studies suggest the present results are invariant to grid and algorithm for modest changes.

PRESSURE (REYNOLDS NUMBER) SCALING

The simulations are focused on approximating the experimental case (examined at IIT by Dr. Ganesh Raman) of a 35 psig supply pressure. Since the supply tube ultimately vents to atmospheric conditions, we can expect the supply tube to contain choked flow. To reduce

the computational requirements, the freestream pressure in the simulations is reduced to 0.03 psia. The ratio of the supply pressure to the freestream pressure is the same ratio as in the laboratory study. The net effect of this scaling of the pressure is to reduce the effective Reynolds number by a factor of 490. The reduced Reynolds number permits a direct numerical simulation with a more modest grid. This scaling results in a number of grid points that permits complete numerical solutions and post processing of a single case to be completed in about one week using 2 processors on a 1.6GHz (per processor) AMD system. Simulations at the laboratory conditions would require a grid wi th 490 times as many points in two dimensions and the simulation times would increase by a factor

of 410 . Solutions are obtained using the WIND code described in a later subsection. SIMULATION RESULTS Data from the PRT actuator experiments at IIT is presented in Fig. 1. The quantity plotted is the actuator resonance frequency, as a function of resonance tube depth, for a supply pressure of 35 psig and a resonance tube diameter of ¼ in. Results are shown for a range of integration slot widths. The primary quantity that determines the resonance frequency is seen to be the resonance tube depth. The width of the integration slot has little influence on the resonance frequency for large tube depths, but becomes more important as the tube depth decreases. The resonant frequency is influenced by the supply pressure for the L/D dimensionless resonance tube depth of 1.5 examined here. Later in the paper these frequency variations will be presented. Two theoretical predictions of the resonance frequency are also shown in Fig. 1. The basic theory is the standard ¼ wavelength resonance frequency, for an open-closed resonance tube. The experimental data is in good agreement with the basic theory for long tube depths, but gradually diverges from the basic theory as the depth of the resonance tube decreases. In order to develop a better understanding of this behavior, we developed a refined theory (Kerschen 2001) that considers the acoustic coupling of the resonance tube and the integration slot. The prediction of this refined theory for an integration slot width of ¼” is shown in Fig. 1. The refined theory is in much better agreement with the experimental data, remaining quite accurate even at small values of

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the tube depth. Essentially, for small tube depths, the inertia of the fluid in the integration slot becomes important, significantly reducing the resonance frequency relative to the prediction of the basic theory. The numerical simulations of the PRT actuator have been carried out for a tube depth of 3/8”, an integration slot width of 1/4”, and a supply pressure of 35 psig. (adjusted by the pressure scaling discussed above). The resonance frequency obtained in the simulation, F = 7.6 kHz, is also shown in Fig. 1. The result is seen to be in good agreement with the experimental data and refined theory. The simulation also determines the amplitude of the resonance. Accounting for the pressure scaling discussed above, the simulation result corresponds to an amplitude of 160 dB, in fairly good agreement with the laboratory value of 157 dB. The simulations also provide details of the unsteady flow inside the actuator, and the external acoustic radiation. A typical sound radiation field, characterized by the far field, is shown in Fig 4. The simulation shown in Fig. 4 is based on viscous no-slip boundary conditions, which will be shown to be quite important. The fields in Figs. 4a,b,c are snapshots spanning approximately one period of oscillation, after the calculation has advanced 31,400 timesteps. At this point in the calculation the field has advanced approximately 17 periods of the basic 7.6 kHz resonance. In the first wavelength (approximately 1¾”) from the integration slot, some asymmetries are present. As the pressure wave moves into the farfield, the evolution shows stronger radiation to the left than to the right. One possible explanation is that the asymmetric flow in the integration slot turns the acoustic waves to the left. A more detailed perspective of the source field is given by the corresponding Mach contours in the supply tube, integration slot, and resonance tube, shown in Figs. 4 d,e,f. There are two major points from Figs. 4 d,e,f. First note that the flow in the integration slot is almost entirely confined to a narrow channel up the wall on the resonance tube side. This feature is present in all snapshots examined. The second important point is that the shock structure oscillates back and forth across the integration slot, varying in extent from as far as 7/8 of the distance across the integration slot to as little as ¼ of the distance across the integration slot.

An alternative problem formulation using slip wall boundary conditions was executed to gain further insight into the physics of this problem. From these alternate formulation results, we speculate that the unsteady chamfer separation is driven by the acoustic resonance, and that the unsteady separation in turn drives the unsteady shock system thereby closing the loop. It is observed that the location of the separation point on the chamfer oscillates significantly during the resonance cycle; the separation on the chamfer can occur as early as ¼ of the chamfer distance or remain attached to the end of the chamfer. The periodic nature of the f low and acoustic field is illustrated by a pressure measurement, taken at the bottom of zone 4 about ¼” from the edge of the integration slot (as was done in the laboratory measurements at IIT). Figure 5 shows the time history of the pressure and its basic periodic nature over the first 30,000 timesteps of evolution of a slip wall calculation, compared with the first 30,000 timesteps of a viscous wall calculation. Comparison of these slip and no-slip cases suggests that the flow separation of the supply jet is very important. One additional difference between the computations and experiments concerns details of the geometry. The computational supply jet issues from a smooth contraction as previously described. In contrast, the experimental geometry contains a sudden contraction. Losses for a sudden contraction in incompressible flow are approximately 35% based on the information in Blevins(1984). The computational frequency response discussed below suggests that the experiments at IIT have a 24% system loss. The direct experimentally measured loss was 28.4% (see Khanafseh et al. 2002). The presence of a Mach 0.5 freestream flow and boundary layer external to the PRT reduces the resonance frequency by 12% and increases the SPL by 3dB, relative to the no flow case. These changes are caused by the modified acoustic impedance of the integration slot exit in the presence of the external stream, and possibly also by changes to the mean flow within the slot. The pressure history for this case at the same spatial point as the no freestream case is given in Fig. 6. The freestream pressure and supply pressure were both doubled for the case displayed in Fig. 6; the pressures were increased to raise the Reynolds number. Unfortunately the

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Reynolds number is still too low for amplified instability waves to exist in the external boundary layer. Finally we discuss the effects of nozzle pressure ratio (NPR) on the behavior for a “shallow” resonance tube which has a “depth to diameter ratio” of 1.5. At an NPR of 2.0 the flow exits the supply jet at nearly sonic velocity and no resonance develops. Increasing the NPR to 2.5 produces a supersonic exit flow but still no resonance develops. At NPRs of 3.0, 3.5, and 4.0, strong resonances develop. At higher NPRs the flow again becomes steady after the transient dies out. These behaviors are illustrated in Table 1 and Fig. 7. The experimental studies of Khanafseh et al. (2002) reveal that in some cases a change in NPR can produce mode shifts with higher harmonics becoming dominant, though usually with reduced amplitude. The computational resolution appears insufficient to capture the shift to the experimentally observed third harmonic.

THE WIND CODE These simulations were performed using the flow solver WIND. WIND is a general purpose Euler and Navier-Stokes solver. WIND is available to the public through the NPARC consortium (lead by NASA GRC and AEDC). Explict Runge-Kutta third-order time integration is used in the present time-accurate calculations.

Based on the paper by Cain & Bower 1995 the fifth order scheme was selected as the best available in WIND for acoustic propagation problems. The paper by Cain et al. 1998 successfully applies the capabilities of the WIND code to the receptivity problem with a good match to results from linear theory. However, the importance of numerically transparent zone boundaries dictated use of the third order scheme for the work presented here.

CONCLUSIONS Active Flow Control (AFC) offers important new capabilities for applications. However, actuators with high bandwidth and strong authority are required. The powered resonance tube (PRT) concept, which involves a high-speed jet that impinges on the open end of an open-closed

resonance tube, is an attractive actuator for AFC. This PRT actuator is capable of producing flow oscillations of high amplitude and high frequency. Direct numerical simulations of the unsteady flow in the PRT actuator were carried out in order to explore the flow physics and better understand the fundamental mechanisms responsible for the resonance. Scaled simulations of the powered resonance have been achieved with good correspondence to laboratory experiments in terms of the frequency (simulated at 7.6 kHz) and amplitude (a simulation value of 160dB) of their resonant response. The laboratory experiments were performed at Illinois Institute of Technology and are described in Raman et al. (2002) and Khanafseh et al. (2002). The simulations suggest new insights into the complexity and details of the flowfield. The simulations show that the flow in the integration slot is primarily on the resonance tube side with almost no flow on the supply tube side of the integration slot. The numerical results suggest that the acoustic waves from resonance in the resonance tube drive an unsteady separation at the supply tube. The unsteady separation at the supply tube in turn drives the observed large oscillations in the shock structure. The unsteady separation seems to be a key aspect of the resonance phenomena. For shallow resonance tubes, the frequency is influenced by the nozzle pressure ratio (NPR). The resonance develops only above a lower threshold NPR, and ceases to resonate strongly above an upper threshold NPR. Finally, the presence of a Mach 0.5 stream adjacent to the PRT produced boundary layer pressure fluctuations at a resonant frequency 12% below that for no external stream, while increasing the amplitude by 3dB. Analytical modeling of the acoustic resonances in the PRT geometry (Kerschen 2001) was carried out in order to understand how the geometrical parameters influence the resonance frequency. For the smaller tube depths associated with higher resonance frequencies, the integration slot geometry was found to play an important role in determining the resonant frequency.

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ACKNOWLEDGEMENTS This work was supported in part by AFOSR STTR contract F49620-00-C-0046 under the Program Management of Drs. Steven Walker and John Schmisseur. REFERENCES Blevins, R. D., Applied Fluid Dynamics Handbook , Published by Van Nostrand Reinhold Company, 1984. Cain, A. B., Rogers, M. M., Kibens, V., and Raman, G., “Simulations of High-Frequency Excitation of a Plane Wake,” AIAA-2001-0514, Presented at the AIAA Aerospace Sciences Meeting, Reno, NV, Jan., 2001. Cain, A. B., Vaporean, C. N., and Parekh, D. E., “Computational Characterization of Receptivity in Jet Flow Control,” ASME FEDSM98-5310, Washington, D.C., June 1998. Cain, A.B. and Bower, W.W, "Comparison of Spatial Numerical Operators for Duct-Nozzle Acoustics," Proc. of the Computational Aeroacoustics Workshop (NASA Langley), 1995. A.B. Cain, E.J. Kerschen, and G. Raman, “Simulations of Acoustic Characteristics and Mechanisms of a Powered Resonance Tube,” AIAA 2002-2400, AIAA/CEAS Aeroacoustics Conference, Breckenridge, CO , June, 2002. Greenblatt D, Wygnanski IJ, “The control of flow separation by periodic excitation,” PROGRESS IN AEROSPACE SCIENCES, 36 (7): 487-545 OCT 2000.

Kastner, J and Samimy, M., “Development and Characterization of Hartmann Tube based Fluidic Actuators for Flow Control,” AIAA 2002-0128; to appear in AIAA Journal. E.J. Kerschen, “"Analytical modeling of the resonant frequencies of a powered resonance tube,” Division of Fluid Dynamics of the American Physical Society Meeting, Nov. 18-20, 2001, San Diego, CA. Khanafseh, S., Raman, G, and Cain, A. “High Bandwidth Actuators for Flow Control Applications,” AIAA 2002-2820, 2002. Nishri, B. and Wygnanski, I. 1998 "Effects of periodic excitation on turbulent flow separation from a flap," A.I.A.A. J. 36:547-556. Raman, G., Khanafseh, S., & Cain, A. 2002, “Development of high bandwidth actuators for aeroacoustic control.” AIAA Paper 2002-0664. Stanek, M., Raman, G., Kibens, V. & Ross, J., 2000, “Cavity tone suppression using high frequency excitation,” AIAA 2000-1905, 6th AIAA/CEAS Aeroacoustics Conference, June 2000, Lahaina, Hawaii. Stanek, M., Raman, G., Kibens, V., Ross, J., Peto, J., and Odedra, J. 2001 Suppression of cavity resonance using high frequency forcing - the characteristic signature of effective devices. AIAA paper 2001-2128. Wiltse, J.M. & Glezer, A., 1998, “Direct excitation of small-scale motions in free shear flows,” Phys. Fluids, vol. 10, pp. 2026--2036.

Table 1 NPR Freq 2 NR 2.5 NR 3 6491 3.5 7620 4 7938 4.5 NR 5 NR Table 1 presents frequency as a function of the nozzle pressure ratio. NR denotes no resonance.

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Figure 1 Experimental data base of actuator frequency versus actuator depth is shown with one simulation data point and the curve for the basic theory. More refined theoretical results have been obtained and show improved agreement.

Fig. 2 A close-up view of zones 1-3. Supply tube is zone 1 with 101X21 points, zone 2 is the integration slot with 41X101 points, and zone 3 is the resonance tube with 61X21 points.

Basic Theory

Computational Data Point

Frequency vs. Depth at 40psig

0

5

10

15

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25

0 0.2 0.4 0.6 0.8 1 1.2 1.4

depth (in)

freq

. (kH

z)

0.2" sp.

0.3" sp.

0.4" sp.

0.5" sp.

0.6" sp.

theory

simulation point

Kerschen Theory

Simulation point at 0.25” spacer, 3/8” depth. (7.6kHz &160dB)

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Fig. 3 The 4 zone grid used for the powered resonance tube simulations. Zone 4 is the far field with 201X101 points. In some case a 3/8” wall is present in the lower left corner with a Mach 0 .5 flow passing over it. The flow reattaches before reaching the integration slot. The purpose of the wall is to thicken the boundary layer and increase the Reynolds number. Zones 1-3 as described in Fig. 2.

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a) pressure after 31,400 timesteps

b) pressure after 32,200 timesteps

c) pressure after 33,200 timesteps

d) Mach contours after 31,400 timesteps

e) Mach contours after 32,200 timesteps

f) Mach contours after 33,200 timesteps

Figure 4 Pressure and Mach contours over approximately one period of oscillation in a simulation after about 15 prior periods of oscillation. The Mach contours show the movement of the shock system and the quiescent region in the integration slot.

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Figure 5 A time trace of the pressure in the far field with the solid line ____ corresponding the case that produced the snapshots shown in Figure 4 and the dashed line ----- corresponding to a slip wall calculation. There is no mean freestream flow in this calculation.

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Figure 6 Pressure oscillations on the wall in a Mach 0.5 freestream and boundary layer driven from below by a powered resonance tube. The pressure is measured at the same location as in Fig. 5, but the the mean pressure is doubled.

Frequency as a function of NPR

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Figure 7 Resonance frequency as a function of nozzle pressure ratio (NPR) for a “shallow” resonance tube.